I was just wondering, because I loosely remember from your introduction post that you enjoy the classic Lemmings experience: Are you aware of Cheapo lemmings?
It's a lemmings engine that was quite popular before the Lemmix times. It only features the classic 8 skills, and I think the only special object that behaves differently from traps is an antigravity object (and rarely any level ever uses it). There is support for custom styles, and there is a replay feature akin to WinLemm, but other than that I don't think it has many fancy features. The title screen might be a bit of a turn off at the beginning, but the gameplay feels very classic and a lot of excellent levels have been made for this engine.

The download is available in this post. The website only has a few levels, but if you're interested I can dig out a few nice level packs from my hard disk.

I see the points either way, and at this point I don't really know which I prefer, but there are three reasons why when you first changed it I found it a bit jarring.

- Game just stops when the last lix dies but you haven't saved enough. The indication of what is going on is just a small text in the task bar, and I was confused at first. I generally also used to restart the level and fast-forward rather than step back a few seconds, so the advantage of having the latter option wasn't really of much value to me, though objectively I guess it should be considered as a plus. I think back when the dialog appeared, I was used to just pressing Space to retry, and now I have to press a hotkey that's slightly more out of the way, but this is a personal issue and shouldn't be held in favor of or against this.
- It's definitely less evident where the stats from your last try are displayed. The menu already has so much information that it stands out less, and because the context is wider, it is probably also less clear what it actually means. ("99 Lix saved" is reasonably clear, but strictly speaking could also refer to your personal best or something like that.)
- Data loss. If you don't have auto-saving enabled, the "Save replay" button is similarly hidden like the stats. Easy to miss and once you swap to a different level, your replay is lost.

Let me upload my challenge replay archive here, I used to download pretty much every replay back in the day until some point, so you might find some of the missing replays in there.
For the "Skills you can't live without" challenge the subfolder is ch_mineachtype.
(I only grabbed all .lrb files, so this might be missing a few replays contained in zip archives which I didn't unzip. I checked the subfolder ch_mineachtype and at least this one is complete though.)

For starters - what happens with the inbetween pixels? For example - a faller moves down 3 pixels per frame. A jumper could make a total of up to 6 "one pixel horizontal or vertical" movements in a single frame - and possibly more vertical movement at the end under specific conditions when hitting a wall as a climber / close to the top.

But the thing that really set off alarm bells for me here is the fact that the placed terrain could interfere with the lemming's own movement. Of course, ideally, it wouldn't, but special handling would be needed to ensure that - especially in cases where it might affect future frames.

I specifically mentioned a 4x4 block of terrain, not a single pixel. That's why I was surprised you'd mention the jumper specifically; does it move more than 4 pixels horizontally or vertically in a single frame? For example, a vector of (3,4) or (4,3) pixels would still be fine with the blocks connecting to each other and being walkable. (Of course, it doesn't have to be 4x4: I chose it because 4 pixels high would ensure lemmings following the main lemming would not get stuck in its terrain). Implementation-wise I would have thought you'd just cache the last (say) 3 or 4 positions of the lemming, and then place the block in the location the lemming was 3 or 4 frames ago, which would make sure the lemming wouldn't bump into its own terrain unless it's moving slower than 1 pixel per frame or changing direction.
So the cases you'd have to worry about would be the slow skills, and directional changes (horizontal and vertical). I believe that these can be solved by specifying a position offset for certain action types: E.g. so climbers don't get stuck in the terrain they create, the blocks could be placed, say, 2 pixels below their effective coordinate. (I guess you could also specify different delays per skill, but I think that would be more complicated and more error prone for skill transitions). That would keep the skill conceptually simple and predictable for players and at the same time make it simple to implement.

For the slow skills:
- I guess terrain creators wouldn't be too much of a concern as if you assign it to a builder and it immediately stops, so be it, applying it to terrain creating skills isn't really a use case.
- Terrain destroyers wouldn't really be affected, just possibly leave a little trail in their tunnel (for diggers and miners, depending on your offset of choice, you could allow them to continue working in mid-air by creating terrain under them if you wanted that behaviour).
- The disarmer stays still for a while, so it would create terrain around itself and then move up onto it when transitioning into walker, creating a little bump; I'd argue that's a corollary of the rules and totally fine.
- Climber I just discussed.

For directional changes:
- Walker turning around (against wall, blocker, or walker skill assignment): should play nicely with the parameters above. The walker would walk up onto its terrain block from 4 frames ago 2 frames after turning around, continuing a nice smooth trail.
- Terrain creators or removers turning on a blocker: see above
- Glider bumping into wall: Not sure how the collision works exactly, but with an offset slightly above it should be possible to have the glider glide under its previously created bridge due to the delay.
- Jumper jumping against wall: depending on whether the jumper is in its upward or downward phase, it might end up landing on its trajectory trail or jump under it. That's a corollary of the physics and seems like fine behaviour to me.
- Climber reaching top and falling down: due to the delay/offset it should land on its pile below and walk off it.
- Shimmier jumping up without reaching ceiling: Same as climber. With repeated assignment could be used to reach higher ceilings

I would guess that by choosing a good delay value and specifying appropriate offsets you would get good behavior for all reasonable cases, avoiding the need for special case handling. Finding these offsets might take a bit of experimentation, but wouldn't add to the code complexity.

In fact, I'm pretty sure if we exclude Kieran's levels (just to get a sense of how other people designed their levels), the remaining custom L2 levels in this forum either never used the bazooka/mortar, or maybe at most one or two levels did.  At least that's how I remember it, feel free to correct me though. 

I remember making "Friendly Fire", but that exclusively relied on the knockback effect of the bazooka. I believe you can use the bazooka/mortar also to pop balloons, but that obviously wouldn't be a concern in NL.

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This seems more to me like an argument against any further new skills than against the Slider specifically.

I am also totally fine with that to be honest!

Haha, that's what I was talking about in my first post in this thread.

Reading (and misunderstanding) the proposition of the creator gave me a different idea for a very versatile skill that could in particular increase the value of any existing movement skills:
The trailer/tracer: Once assigned, for a fixed amount of time (e.g. 2 seconds) it would, each frame, place a small block of terrain (say 4x4 pixels) at its current position (above its feet). In other words, it would trace out the trajectory of the lemming with a terrain trail for 2 seconds.
Examples:
- with a walking lemming, it would simply elevate the floor by 4 pixels
- with a jumper, it would create a bridge between the jump starting point and its destination
- with a hang glider, it would make a slope that lemmings can walk up or down
- with a faller or floater, it would create a wall that can be climbed
- with a shimmier, it would create a platform below the ceiling (not sure how useful that is...)
- walking over a shallow digger hole that's currently being dug, it could plug up the digger's hole.
- with a swimmer it could close up a water gap

I guess it would make the stoner somewhat redundant, though it would bring a lot of new things to the table to be a valuable addition regardless. (Also see discussion below.)
Furthermore a weaker skill is not entirely useless, sometimes the levels designer might want to give the player a weaker skill to prevent alternative solutions.

The slider overrides normal rules at some future time: The next/every time the lem would fall, the lem slides instead. This breaks mental pathfinding. The skill must bring a ton of design goodness to overcome this massive burden.

I consider this a boon rather than a burden for the slider. Having the slider turn always around was core to many puzzles in QFK, and I found it to be quite refreshing.
That said, it is true that the glider can provide this feature with appropriate terrain design (i.e. a wall that the glider bumps into and turns around), and in that sense makes the slider a weaker addition to NL than it is in L2. It still has the link-up with the shimmier going for it which you can't replicate with any other skill, but maybe that's not enough.

I'm happy to see that Kieran has chimed into the discussion, if anyone he should be the authority on the usefulness of L2 skills.
It seems like we agree on the rather limited use of the laser blaster and projectile terrain creation skills, though I also personally find the use of projectile terrain destruction skills rather limited as well from my experience.

Simon's proposition of the angled laser blaster seems definitely better than either of those. Fast upward gain seems to be something new, and at the same time with a sufficient blasting range it could emulate the ability to make dents in remote walls or ceilings of projectile destructive skills without having the liability of their rather awkward projectile arc.
I guess like projectiles it could be nerfed by making the laser beam lethal; at the same time it poses the risk of making certain things possible but fiddly, e.g. timing the blast into terrain populated by lemmings in such a way that no-one gets hurt, something that a level designer cannot rely on for backroute prevention, but at the same time won't want the player to require doing.

With regards to this making the fencer redundant: As before, I don't think that should be an argument against a skill if it brings enough new things to the table. It might just mean that the fencer shouldn't have been in the game in the first place; in many instances a basher does the job just as well too.

Permanents introduce state that is hard to see, and come with lots of special interaction rules. Have too many permanents, they'll get in each other's scope, and thus the need for rules grows quadratically.

And permanents have a higher chance to turn out the weakest in hindsight. The floater is the weakest skill in Lemmings 1. Runner and floater are the two weakest skills in Lix. The disarmer is the weakest skill in NL.

Just because some engines made bad choices in which permanent skills they chose doesn't mean that permanents generally make bad choices. The climber is one of the best skills. I rather think that their limitation is that they basically have to be movement skills, so you cannot have too many very unique ones of those. So if you do have many of them it's very likely that some of them suck or are redundant. But that just means that they need to be chosen wisely. One unique thing they bring to the table is that they allow you do to multiple things with a single assignment, which I think is always a good feature to have in a level. The floater is weak because you need to put a lot of effort to make use of it more than once. The runner is weak because it doesn't do anything (in L2 it would hop over small gaps, setting it apart from the rest of the crowd at least). The disarmer and swimmer are weak because their use cases are so very specific. I'm pretty sure if there'd been a lengthy discussion like now, the runner wouldn't be in Lix and the swimmer wouldn't be in NL.

The climber, glider, slider and L2 runner all bring good features to the table with a lemming having that skill easily employing its feature multiple times in a level. On their own they are great, but with the jumper in the game the L2 runner becomes less unique, and similarly with the glider in the game the slider becomes less unique. It always depends on the context. Now if a new skill is more versatile but makes another one redundant, that's more a point saying the old one shouldn't have been there in the first place rather than a point against the new skill. But with things being the way they are and skill cullings being quite unlikely, in practice it might make the new skill a less attractive addition even if it is a good one.

4 PM Eastern is 8 pm UTC/9 pm UTC+1, works for me, though I wouldn't mind if someone wanted to start a bit earlier already.

I'm pretty flexible, anything between 7 and 11 pm UTC+1 should definitely go and earlier probably as well.

Just wanted to chip in as I've played Quest from Kieran in Lemmings 2 which heavily featured the slider in one or two tribes as well as the bazooka/mortar/laser blaster (and which I recommend everyone to play btw, it's an excellent pack):

The slider was crucial to many puzzles. In particular, the fact that the slider is a permanent skill and that it turns around at the bottom of a cliff would separate it from lemmings walking the same way, which could be key to solutions or foil various other solution attempts. Unlike the floater, it can't get down a thin platform high above the floor, but on the other hand can be used to get down to a lower platform if two platforms are on top of each other and their edges are aligned, and in conjunction with the shimmier it can climb on the underside of platforms (I believe it also slides down walls if a shimmier bumps into a wall). I don't know how the jumper interacts with the climber in NeoLemmix (climber sticks when jumping into a wall? climber can jump off a wall?) but if these behaviours are implemented, the slider could be consistent with those (i.e. starting to slide when jumping into a wall/slider can jump off walls).

Both mortar/bazooka and laser blaster on first glance seem more useful than the slider, but after playing QFK the slider is definitely more memorable to me, somehow.

On a more general note, "20 is a nice round number" is a horrible reason to have exactly 20 skills. I would argue if the discussion doesn't bring up any fully convincing skill sticking with 19 is preferable; similarly if multiple very strong candidates come up (they might even interact or complement each other in some way) then adding more than 1 is preferable.